The first "diagram" has two points (from which the distance will be taken).
If the distances, summed up, are higher than the distance between the two points, you have what happens right there, you have a "virtual circle" of possible points.

They all will have the same distance from the two points.

The three blue dots are on the same plane where the red dots are, one higher, one lower, and they still have the same distance.

Now that was highly simplified, because I made it in 2D when it was supposed to be made in 3D.

Ah, we were thinking in different dimensions.
I was thinking in 2D and you in 3D.
So we were both correct.
I was thinking in terms of cellphone tracking, where only two of the dimensions are important.

Psychologists have shown that children who call people names (like "nerd", "dork", etc.) do it because they have a low self-esteem and feel inferior to the person they are mocking and are trying to lift themselves up.